The accurate measurement of wall shear stress remains a challenge in many industrial applications as well as in scientific research. Precise knowledge of shear stress can benefit many fields of human activity. For example, it can (a) reduce the cost of manufacturing and increase quality and throughput of certain products in the pharmaceutical, food, paint, and coating industries, and (b) improve the performance of aircraft. The real-time measurement of the local wall shear stress is important whenever dynamic flow control is required. Despite the long history of wall shear force measurement attempts using various approaches, the state of the art is still insufficient to meet all needs.
The ways of measuring shear stress fall into three categories: Indirect, Semi-Direct and Direct.
Most of the available sensors for measuring shear stress use indirect measurement techniques where the wall shear stress is inferred, through a set of assumptions, from another flow property, such as, for example, streamwise velocity or heat transfer rate, measured at or near the wall. These Indirect measurement methods include, for example:                hot-wire/film-based anemometry (U.S. Pat. No. 5,883,310)        laser-based near-wall flow velocity measurements (D. Fourguette, D. Modarress, D. Wilson, M. Koochesfahani, M. Gharib, “An Optical MEMS-based Shear Stress Sensor for High Reynolds Number Applications,” AIAA-2003-742, 41st Aerospace Sciences Meeting and Exhibit, Reno, Nev., Jan. 6-9, 2003)        
To retrieve information about shear stress, the indirect methods for measuring shear stress require precise modeling of the flow near the wall and knowledge of flow parameters such, as temperature and viscosity. For most applications, these models are not developed sufficiently well and the parameters are not well known. Laser-based flow velocity methods also require the fluid to be sufficiently transparent for the laser radiation, thus restricting the field of applications of these methods.
Another method, that can be classified as Semi-Direct and that has been frequently used in aerodynamic applications, is the surface oil-film/liquid-crystal interferometry (see, for example, U.S. Pat. No. 5,438,879). This approach, however, does not provide dynamic measurement of the wall shear stress and the spatial resolution can be poor. Technically, this approach requires covering an extended part of the wall with a film and having optical access to the film that can be difficult to implement in applications other than aerodynamic. Also, for high levels of shear stress the film may be susceptible to mechanical damage.
Direct wall shear measurement techniques are preferable because they measure a motion of a floating element, positioned flush within the wall, that is directly caused by the shear force (U.S. Pat. No. 4,464,928). In these methods, the measurement of the floating element displacement is measured that is accomplished by a number of techniques:
A. Electrical                Piezoresistive—In this approach, the shift of the floating element causes deformation of the piezoresistive element that is translated into electric signal (see, for example, J. Shajii, K-Y. Ng, M. Schmidt, “A Microfabricated Floating Element Shear Stress Sensor Using Wafer-Bonding Technology,” Journal of Microelectromechanical Systems, V.1, No. 2, 1992, pp. 89-94)        Capacitor-based—In this approach, a floating element is mounted on one of the capacitor plates, so that the shift of the floating element changes the capacitance and this change is measured by electrical/electronic means (for example, M. Schmidt, R. Howe, S. Senturia, J. Artitonidis, “Design and Falibration of a Microfabricated Floating-Element Shear-Stress Sensor,” IEEE Transactions on Electron Devices, v35, n6, 1988, pp. 750-757). These miniature electrical shear stress sensors, while showing satisfactory results in laboratory tests, to date have found limited applications due to following drawbacks:        (1) Small dynamic range of shear stress measurement        (2) Susceptibility to electromagnetic interference        (3) Low sensitivity for piezoresistive MEMS sensors        (4) For capacitance-based sensors, it is intrinsically difficult to separate shear stress from pressure (or from the force directed normal to the floating element surface)        
B. Optical                Optical position measurement—In this approach, the floating element is illuminated from above and the shift is measured by an array of photodiodes placed below the element (A. Padmanabhan, M. Sheplak, K. S. Breuer and M. A. Schmidt, “Micromachined Sensors for Static and Dynamic Shear-Stress Measurements in Aerodynamic Flows,” TRANSDUCERS '97, 1097 international Conference on Solid-state Sensors and Acfuators, Chicago, June 16-19, pp. 137-141, 1997).        The basic difficulty of this method is the requirement of flow to be transparent for the illuminating laser radiation that should be arranged externally. This method is similar in design to the oil film sensing described above.        Optical resonance methods—These methods rely on the deflection of an optical beam to convert any change in a mechanical attribute of a structure (for example, a displacement of the cantilever supporting the floating element) into the resonance frequency shift. Most popular shear stress sensors of this type are fiber-based Fabry-Perot interferometers (U.S. Pat. No. 6,426,796 B1).        The optical resonance methods are immune to electromagnetic radiation and can be realized in a size that is not larger than MEMS shear stress sensors described above. The fiber-based Fabry-Perot sensors, however, require a delicate mechanical alignment of the resonator (for example, rotational motion of the floating element may cause significant loss of the resonant signal quality). Another problem is the need for the Fabry-Perot resonator to be optically clean, a condition that is difficult to sustain in many applications.        
The most important drawback of all known direct shear stress measurement methods is the requirement of a sizeable gap between the floating element and the wall, to give room for the floating element to shift under the shear force. This gap needs to be greater than at least 100 micrometers for all the described methods, to measure up to two orders of magnitude in shear stress (with the exception of the fiber-based Fabry-Perot interferometry). Most liquids penetrate holes larger than approximately 1 micrometer. Therefore, in all existing direct measurement shear stress sensors, the liquid will make its way into the internal elements of the sensor and will fill the gap. This may cause the inner elements of the sensor to malfunction and may impede the motion of the floating element. The problem can be solved by inserting a material between the floating element and the wall or by covering the gap from the side of the flow with a flexible material, however, that decreases sensitivity of the sensor and may be unsuitable for chemically active flows.
The drawback of the direct method is overcome in the approach that is commonly known as “whispering gallery modes” (WGM) optical measurement technology. Like the Fabry-Perot interferometry method, the WGM technology is based on observing changes in the spectrum of a resonator that is subjected to the external force. Instead of using an open resonator, as it is done in the Fabry-Perot interferometry, WGM employs dielectric micro-resonators (such as a glass sphere) with light captured inside. A minute change in the size, shape or refraction index of the micro-resonator alters the spectrum of the micro-resonator that manifests itself as a shift in its resonant frequency, a change in the magnitude for a particular resonance or in emergence of additional resonances in the spectrum. The micro-resonator spectrum can be measured, for example, by using a tunable laser and an optical detector. Usually, the shifts of the resonances are most practical to measure. Therefore, the discussion below is restricted to measuring the resonance shifts. The other features of the WGM spectra could also be employed in the method.
The optical resonances, or “whispering gallery modes” (WGM), are extremely narrow. Thus very small shifts of WGMs can be detected, which may be used for the precise measurements of the force causing the shifts (M. Kozhevnikov, T. Ioppolo, V. Stepaniuk, V. Sheverev and V. Otugen, “Optical Force Sensor Based on Whispering Gallery Mode Resonators,” AIAA-2006-649, 44th AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nev., Jan. 9-12, 2006). It has been shown that a change of a micro-sphere diameter as low as 0.01 nm can be detected by observing WGM shift (Ilchenko, V. S. et. al., “Strain-tunable high-Q optical microsphere resonator,’ Optics Communications, 1998. 145(1-6): p. 86-90). That provides an opportunity for designing a floating element shear-stress sensor with an extremely narrow gap between the floating element and sensor wall. For example, for a gap of 100 nm that is not penetratable by any liquid, three orders of magnitude for the force can be measured.
A design for a shear stress sensor based on optical micro-resonators was proposed by Otugen & Sheverev (V. Otugen, V. Sheverev, U.S. patent application Ser. No. 11/926,793 (November 2007, see also M. Kozhevnikov, T. loppolo, V. Stepaniuk, V. Sheverev and V. Otugen, “Optical Force Sensor Based on Whispering Gallery Mode Resonators,” AIAA-2006-649, 44th AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nev., Jan. 9-12, 2006). In this design, the micro-resonator is placed between a movable floating element and the wall of the sensor, so that the micro-resonator effectively serves as a floating element support. Such an arrangement leads to the increased sensitivity of the sensor to the force acting normal to the surface of the floating element. This force may shift the floating element in the direction normal to the flow and change the position of the micro-resonator relative to the optical waveguide. The efficiency of the coupling will be affected which may lead to the WGM resonance shift caused by a normal force rather than shear force and, thus, to a false reading of the shear stress measurement.